By on the analyzing the general structure of the Green function of a strongly correlated electron system, it is shown that, for the regime of strong correlations, Luttinger’s theorem should be generalized in the following way: the volume of the Fermi surface of the system of noninteracting particles is equal to that of the quasiparticles in the strongly correlated system with due regard for the spectral weight of the quasiparticles. An investigation of the t-J model and of the Hubbard model, as applied to the paramagnetic nonsuperconducting phase, shows that the generalized Luttinger theorem is valid for these models.
Molecular periodic systems have the challenge of not only representing an infinite, albeit periodically repeating, molecule but also treating the strong electron correlation that emerges in such systems. Many post-Hartree-Fock methods that are efficient in moderately correlated molecules often fail to describe strongly correlated electrons and their properties in periodic systems. Here we develop and apply an electronic structure approach to periodic systems based on the variational calculation of the two-electron reduced density matrix (2-RDM). The variational 2-RDM method calculates a lower bound to the ground-state energy of a molecular periodic system without computation or storage of its many-electron wave function. The 2-RDM is constrained by
N-representability conditions that are necessary for it to represent at least one
N-electron density matrix---conditions that allow it to treat strongly correlated systems. Two periodic systems are treated to demonstrate the methodology: (i) a metallic hydrogen chain and (ii) a strongly correlated acene chain. In the hydrogen chains the 2-RDM theory describes the strongly correlated Mott metal-to-insulator transition while in acene chains it describes the emergence of polyradical character with increasing chain length. The methodology is applicable to treating strong electron correlation in more general periodic molecules and materials.
A two-dimensional mesoscopic Bose system of dipoles in a 2D trap is considered using computer simulation by the quantum path-integral Monte Carlo method. The model describes a rarefied system of spatially indirect excitons in a confining potential. Bose condensation in the system and its superfluid and structural properties are studied over a wide range of interparticle spatial correlations, from an almost ideal Bose gas to the regime of a strongly correlated system. It is found that, at strong interparticle spatial correlations, particles in the condensate form a crystal-like structure. In this case, the spatial correlations of particles in the condensate are less pronounced than the correlations of noncondensed particles. The effect of recurrent crystallization is observed in the regime of strong interparticle correlations.